Can ursodiol cause a metallic taste in the mouth?

Yes. Metallic taste is one of the reported side effects of ursodiol.

Side Effects of Ursodiol - for the Consumer

All medicines may cause side effects, but many people have no, or minor, side effects. Check with your doctor if any of these most COMMON side effects persist or become bothersome when using Ursodiol:

Constipation; diarrhea; dry skin; gas; headache; indigestion; metallic taste; muscle or joint pain; nausea; skin rash; stomach pain; swelling; tiredness.

Seek medical attention right away if any of these SEVERE side effects occur when using Ursodiol:

Severe allergic reactions (rash; hives; itching; difficulty breathing; tightness in the chest; swelling of the mouth, face, lips, or tongue).

see http://www.drugs.com/sfx/ursodiol-side-effects.html